Subgroups — C₄×C₈²×C₂₃ #19155464

Order 5888.

750 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₈×C₂₃	C₂	1	3	yes	maximal
2	C₂×C₈²×C₂₃	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₂₃	C₄	1	12	yes	—
4	C₂×C₄×C₈×C₂₃	C₂²	1	6	yes	—
5	C₄³×C₂₃	C₂²	1	1	yes	characteristic
6	C₈²×C₂₃	C₄	1	16	yes	direct product factor
7	C₂²×C₈×C₂₃	C₂×C₄	1	12	yes	—
8	C₂×C₄²×C₂₃	C₂×C₄	1	6	yes	—
9	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
10	C₄×C₈×C₂₃	C₈	1	48	yes	direct product factor
11	C₄×C₈×C₂₃	C₂×C₄	1	24	yes	—
12	C₂²×C₄×C₂₃	C₄²	1	4	yes	—
13	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
14	C₂×C₈×C₂₃	C₄²	1	24	yes	—
15	C₂×C₈×C₂₃	C₂×C₈	1	48	yes	—
16	C₄²×C₂₃	C₂×C₈	1	24	yes	—
17	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
18	C₄×C₈²	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₂₃	C₂×C₄²	1	1	yes	characteristic
20	C₂×C₄×C₂₃	C₄×C₈	1	24	yes	—
21	C₂×C₄×C₂₃	C₂×C₄²	1	6	yes	—
22	C₂×C₄×C₂₃	C₂²×C₈	1	12	yes	—
23	C₈×C₂₃	C₄×C₈	1	48	yes	direct product factor
24	C₄²×C₈	C₂×C₂₃	1	3	yes	—
25	C₂×C₈²	C₂×C₂₃	1	4	yes	—
26	C₂²×C₂₃	C₄³	1	1	yes	characteristic
27	C₂²×C₂₃	C₂×C₄×C₈	1	6	yes	—
28	C₄×C₂₃	C₈²	1	16	yes	direct product factor
29	C₄×C₂₃	C₂×C₄×C₈	1	12	yes	—
30	C₂×C₄×C₈	C₄×C₂₃	1	12	yes	—
31	C₂×C₄×C₈	C₂²×C₂₃	1	6	yes	—
32	C₄³	C₂²×C₂₃	1	1	yes	characteristic
33	C₈²	C₄×C₂₃	1	16	yes	direct product factor
34	C₂×C₂₃	C₂×C₈²	1	4	yes	—
35	C₂×C₂₃	C₄²×C₈	1	3	yes	—
36	C₂²×C₈	C₂×C₄×C₂₃	1	12	yes	—
37	C₂×C₄²	C₂×C₄×C₂₃	1	6	yes	—
38	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
39	C₄×C₈	C₈×C₂₃	1	48	yes	direct product factor
40	C₄×C₈	C₂×C₄×C₂₃	1	24	yes	—
41	C₂₃	C₄×C₈²	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²×C₄	C₄²×C₂₃	1	4	yes	—
43	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
44	C₂×C₈	C₄²×C₂₃	1	24	yes	—
45	C₂×C₈	C₂×C₈×C₂₃	1	48	yes	—
46	C₄²	C₂×C₈×C₂₃	1	24	yes	—
47	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
48	C₂³	C₂×C₄²×C₂₃	1	1	yes	characteristic
49	C₂×C₄	C₄×C₈×C₂₃	1	24	yes	—
50	C₂×C₄	C₂×C₄²×C₂₃	1	6	yes	—
51	C₂×C₄	C₂²×C₈×C₂₃	1	12	yes	—
52	C₈	C₄×C₈×C₂₃	1	48	yes	direct product factor
53	C₂²	C₄³×C₂₃	1	1	yes	characteristic
54	C₂²	C₂×C₄×C₈×C₂₃	1	6	yes	—
55	C₄	C₈²×C₂₃	1	16	yes	direct product factor
56	C₄	C₂×C₄×C₈×C₂₃	1	12	yes	—
57	C₂	C₂×C₈²×C₂₃	1	4	yes	—
58	C₂	C₄²×C₈×C₂₃	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₄²	C₂³×C₂₃
socle	C₂³×C₂₃	C₂×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. C₈²×C₂₃	C₄	direct (N × H)
10. C₄×C₈×C₂₃	C₈	direct (N × H)
18. C₄×C₈²	C₂₃	direct (N × H)
23. C₈×C₂₃	C₄×C₈	direct (N × H)
28. C₄×C₂₃	C₈²	direct (N × H)
33. C₈²	C₄×C₂₃	direct (N × H)
39. C₄×C₈	C₈×C₂₃	direct (N × H)
41. C₂₃	C₄×C₈²	direct (N × H)
52. C₈	C₄×C₈×C₂₃	direct (N × H)
55. C₄	C₈²×C₂₃	direct (N × H)

Subgroups — C4×C82×C23 #19155464

Conjugacy classes of subgroups

Complements

Subgroups — C₄×C₈²×C₂₃ #19155464